Lesson Objectives
- Demonstrate an understanding of long division
- Demonstrate an understanding of division with decimals
- Learn how to convert a fraction into a decimal
How to Convert a Fraction into a Decimal
In our last lesson, we learned how to divide decimals. This knowledge will enable us to convert a fraction into a decimal. In order to convert a fraction into a decimal:
Example 1: Convert each fraction into a decimal.
$$\frac{3}{4}$$ We will set up our long division with 3 (dividend) under the long division symbol and 4 (divisor) to the left of the long division symbol:
We can see that 4 is larger than 3. This means we will need to place a decimal point after 3 and add a zero to the right in order to divide. Recall that:
3 = 3.0
Remember to bring the decimal point up into the answer:
Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: 
$$\frac{3}{4}=0.75$$ Example 2: Convert each fraction into a decimal.
$$\frac{9}{20}$$ We will set up our long division with 9 (dividend) under the long division symbol and 20 (divisor) to the left of the long division symbol:
We can see that 20 is larger than 9. This means we will need to place a decimal point after 9 and add a zero to the right in order to divide. Recall that:
9 = 9.0
Remember to bring the decimal point up into the answer:
Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: 
$$\frac{9}{20}=0.45$$ Example 3: Convert each fraction into a decimal.
$$\frac{17}{30}$$ We will set up our long division with 17 (dividend) under the long division symbol and 30 (divisor) to the left of the long division symbol:
We can see that 30 is larger than 17. This means we will need to place a decimal point after 17 and add a zero to the right in order to divide. Recall that:
17 = 17.0
Remember to bring the decimal point up into the answer:
Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: 
$$\frac{17}{30}=0.5\overline{6}$$
- divide the numerator by the denominator
- Continue the division until the remainder is zero or a repeating digit/series of digits
Example 1: Convert each fraction into a decimal.
$$\frac{3}{4}$$ We will set up our long division with 3 (dividend) under the long division symbol and 4 (divisor) to the left of the long division symbol:
We can see that 4 is larger than 3. This means we will need to place a decimal point after 3 and add a zero to the right in order to divide. Recall that: 3 = 3.0
Remember to bring the decimal point up into the answer:
Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: $$\frac{3}{4}=0.75$$ Example 2: Convert each fraction into a decimal. $$\frac{9}{20}$$ We will set up our long division with 9 (dividend) under the long division symbol and 20 (divisor) to the left of the long division symbol:
We can see that 20 is larger than 9. This means we will need to place a decimal point after 9 and add a zero to the right in order to divide. Recall that: 9 = 9.0
Remember to bring the decimal point up into the answer:
Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: $$\frac{9}{20}=0.45$$ Example 3: Convert each fraction into a decimal. $$\frac{17}{30}$$ We will set up our long division with 17 (dividend) under the long division symbol and 30 (divisor) to the left of the long division symbol:
We can see that 30 is larger than 17. This means we will need to place a decimal point after 17 and add a zero to the right in order to divide. Recall that: 17 = 17.0
Remember to bring the decimal point up into the answer:
Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: $$\frac{17}{30}=0.5\overline{6}$$ Skills Check:
Example #1
Write each fraction as a decimal. $$\frac{855}{3600}$$
Please choose the best answer.
A
0.459
B
0.2178
C
0.395
D
0.2375
E
0.2643
Example #2
Write each fraction as a decimal. $$\frac{9}{16}$$
Please choose the best answer.
A
0.545
B
0.5625
C
0.6131
D
0.4985
E
0.5137
Example #3
Write each fraction as a decimal. $$\frac{64}{75}$$
Please choose the best answer.
A
0.61437
B
0.5853
C
0.83
D
0.85134
E
0.853
Congrats, Your Score is 100%
Better Luck Next Time, Your Score is %
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